X-ray tube and method having tilted rotation axis

ABSTRACT

A computed tomography system comprises a gantry and an x-ray tube. The gantry rotates about a gantry axis of rotation. The x-ray tube is mounted to the gantry, and comprises a rotatable assembly having a tube axis of rotation. The tube axis of rotation is angularly displaced from the gantry axis of rotation by a tilt angle. Rotation of the x-ray tube about the gantry axis of rotation produces a first moment, and rotation of the rotatable assembly about the tube axis of rotation produces a second moment that opposes the first moment.

FIELD OF THE INVENTION

[0001] The present invention relates generally to x-ray tubes. Moreparticularly, the present invention relates to systems and methods forbalancing mechanical loads in x-ray tubes.

BACKGROUND OF THE INVENTION

[0002] X-ray tubes have found widespread application in devices such asimaging systems. X-ray imaging systems utilize an x-ray tube to emit anx-ray beam which is directed toward an object to be imaged. The x-raybeam and the interposed object interact to produce a response that isreceived by one or more detectors. The imaging system then processes thedetected response signals to generate an image of the object.

[0003] For example, in computed tomography (CT) imaging, an x-ray tubeprojects a fan-shaped beam which is collimated to lie within an X-Yplane of a Cartesian coordinate system and generally referred to as the“imaging plane”. The x-ray beam passes through the object being imaged,such as a patient. The beam, after being attenuated by the object,impinges upon an array of radiation detectors. The intensity of theattenuated radiation beam received at the detector array is dependentupon the attenuation of the x-ray beam by the object. Each detectorelement of the array produces a separate electrical signal that is ameasurement of the beam attenuation at the detector location. Theattenuation measurements from all the detectors are acquired separatelyto produce a transmission profile.

[0004] In known third-generation CT systems, the x-ray tube and thedetector array are rotated with a gantry within the imaging plane andaround the object to be imaged so that the angle at which the x-ray beamintersects the object constantly changes. A group of x-ray attenuationmeasurements, i.e. projection data, from the detector array at onegantry angle is referred to as a “view”. A “scan” of the objectcomprises a set of views made at different gantry angles during onerevolution of the x-ray source and detector. In an axial scan, theprojection data is processed to construct an image that corresponds to atwo-dimensional slice taken through the object.

[0005] Typically, an x-ray tube comprises a vacuum vessel, a cathodeassembly, and an anode assembly. The vacuum vessel is typicallyfabricated from glass or metal, such as stainless steel, copper or acopper alloy. The cathode assembly and the anode assembly are enclosedwithin the vacuum vessel.

[0006] To generate an x-ray beam, the cathode is heated to a temperatureat which the cathode begins to emit electrons. A voltage difference(typically, in the range of 60 kV to 140 kV) is maintained between thecathode and anode assemblies and accelerates the electrons, causing theelectrons to impact a target zone of the anode at high velocity. Uponimpact, a small fraction (less than 1%) of the kinetic energy of theelectrons is converted to high energy electromagnetic radiation, orx-rays, while the balance produces heat. The x-rays emanate from a focalspot of the target zone in all directions, and a collimator is then usedto direct x-rays out of the vacuum vessel in the form of an x-ray beamtoward the patient.

[0007] In the first x-ray tube designs, the anode assembly remainedstationary. However, due to the large amount of heat that is produced(the focal spot of the anode can reach temperatures of about 2700° C.),a rotating anode design has been adopted for many applications.According to this design, the anode assembly includes a rotating diskand the focal spot moves along a target track on the anode. Thisprevents material on the anode from melting, in a manner generallyanalogous to the manner in which waiving one's hand over a candle ratherthan holding one's hand directly over the candle prevents one's handfrom burning.

[0008] Although the rotating anode design is advantageous in that itpromotes heat dissipation, the rotating anode design provides additionalchallenges inasmuch as two rotating systems are employed. Specifically,the x-ray tube comprises a rotating anode assembly that rotates withinthe x-ray tube about a tube axis of rotation, and the x-ray tube itselfis mounted to a gantry which is rotating about a gantry axis of rotation(e.g., which may be aligned with a patient).

[0009] A difficulty that has been encountered is uneven loading ofbearings that support the rotating anode assembly. Rotating anodeassemblies have used a cantilevered design in which the rotating disk ismounted at one end of a rotating shaft, with the other end of therotating shaft being supported by two or more bearing assemblies. As thex-ray tube rotates about the gantry axis of rotation, the resultantcentrifugal force that is applied to the x-ray tube is opposed primarilyby the bearing assembly that is closer to the rotating disk (closer tothe center of gravity), resulting in uneven loading. This is undesirablebecause it causes premature failure of the bearing assemblies,especially the bearing assembly that provides primary opposition to thecentrifugal force caused by rotation of the gantry.

[0010] In order to improve performance characteristics of CT systems, itis desirable to increase the gantry rotational speeds that are employed.Increased speeds, however, increase the bearing loads since centrifugalforce is proportional to the square of the gantry rotational speed.Therefore, the inability to obtain increased gantry speeds withoutpremature bearing failure has become a limiting factor in thedevelopment of CT systems.

[0011] Therefore, an improved x-ray tube and method of balancingmechanical loads in an x-ray tube would be highly advantageous.

BRIEF SUMMARY OF THE INVENTION

[0012] In a first preferred aspect of the invention, a computedtomography system comprises a gantry and an x-ray tube. The gantryrotates about a gantry axis of rotation. The x-ray tube is mounted tothe gantry, and comprises a rotatable assembly having a tube axis ofrotation. The tube axis of rotation is angularly displaced from thegantry axis of rotation by a tilt angle. Rotation of the x-ray tubeabout the gantry axis of rotation produces a centrifugal force that isapplied to the x-ray tube. Rotation of the rotatable assembly about thetube axis of rotation produces a gyroscopic moment that results in anadditional force being applied to the rotatable assembly that opposesthe centrifugal force.

[0013] In a second preferred aspect, a method of operating a computedtomography system comprises producing a first moment that acts upon anx-ray tube, and producing a second moment that acts upon the x-ray tubewhile the first moment is being produced. The x-ray tube being mountedto the gantry. The first moment is produced by rotation of a gantryabout a gantry axis of rotation at a gantry rotational speed. The secondmoment is produced by rotation of a rotating assembly of the x-ray tubeabout a tube axis of rotation. The tube axis of rotation is tilted withrespect to the gantry axis of rotation. The second moment is agyroscopic moment that is produced by precession of the rotatableassembly. The precession occurs by way of the rotation of the x-ray tubeabout the gantry axis of rotation and the rotation of the rotatableassembly about the tube axis of rotation. The tube axis of rotation ofthe rotatable assembly defines an outer surface of a portion of a coneas the rotatable assembly rotates about the gantry axis of rotation.

[0014] In a third preferred aspect, a computed tomography systemcomprises a gantry and an x-ray tube. The gantry rotates about a gantryaxis of rotation. The x-ray tube is mounted to the gantry, and comprisesa rotatable assembly having a tube axis of rotation. The tube axis ofrotation is angularly displaced from the gantry axis of rotation by atilt angle. Rotation of the x-ray tube about the gantry axis of rotationproduces a first moment, and rotation of the rotatable assembly aboutthe tube axis produces a second moment that opposes the first moment.

[0015] Advantageously, in the preferred embodiments, the tilt anglecauses a gyroscopic moment to be produced which can be used to balanceloading in the x-ray tube. Therefore, although it has long been assumedthat the tube axis of rotation and the gantry axis of rotation must beparallel, it has surprisingly been found that this is not necessarilythe case and that in fact introducing a tilt angle can have significantbenefits.

[0016] Other principle features and advantages of the present inventionwill become apparent to those skilled in the art upon review of thefollowing drawings, the detailed description, and the appended claims.

BRIEF DESCRIPTION OF THE DRAWINGS

[0017]FIG. 1 is a pictorial view of a CT imaging system;

[0018]FIG. 2 is a block schematic diagram of the system illustrated inFIG. 1;

[0019]FIG. 3 is a perspective view of a casing enclosing an x-ray tubeinsert;

[0020]FIG. 4 is a sectional perspective view with the stator exploded toreveal a portion of an anode assembly of the x-ray tube insert of FIG.3;

[0021]FIG. 5 is a more detailed view of the anode assembly of FIG. 3;

[0022] FIGS. 6-8 are diagrams showing the operation of the CT systemincluding the x-ray tube and gantry of FIG. 1;

[0023] FIGS. 9A-9B schematically show the assembly of the anode assemblyof FIG. 3 as pertains to axial forces that are developed on front andrear bearings of the anode assembly;

[0024]FIG. 10 is another diagram showing the operation of the CT systemof FIG. 1;

[0025]FIG. 11 is a graph of the anode tilt angle required to maintain aparticular front bearing load at different gantry rotation speeds; and

[0026] FIGS. 12A-12C show forces developed during the operation of theCT system of FIG. 1;

[0027] FIGS. 13A-13C show the operation of the forces of FIGS. 12A-12Cto reduce anode deflection and thereby improve imaging.

DETAILED DESCRIPTION OF THE INVENTION

[0028] Referring to FIGS. 1 and 2, a computed tomography (CT) imagingsystem 10 is shown as including a gantry 12 representative of a “thirdgeneration” CT scanner. An x-ray tube 14 is mounted to the gantry 12 andgenerates a beam of x-rays 16 that is projected toward a detector array18 mounted to an the opposite side of gantry 12. X-ray beam 16 iscollimated by a collimator (not shown) to lie within an X-Y plane of aCartesian coordinate system and generally referred to as an “imagingplane”. Detector array 18 is formed by detector elements 20 whichtogether sense the projected x-rays that pass through an object 22 suchas a medical patient. Detector array 18 may be a single-slice detectoror a multi-slice detector. Each detector element 20 produces anelectrical signal that represents the intensity of an impinging x-raybeam as it passes through patient 22. During a scan to acquire x-rayprojection data, gantry 12 and the components mounted thereon rotateabout a gantry axis of rotation 24.

[0029] Rotation of gantry 12 and the operation of x-ray tube 14 aregoverned by a control mechanism 26 of CT system 10. Control mechanism 26includes an x-ray controller 28 that provides power and timing signalsto x-ray tube 14 and a gantry motor controller 30 that controls therotational speed and position of gantry 12. A data acquisition system(DAS) 32 in control mechanism 26 samples analog data from detectorelements 20 and converts the data to digital signals for subsequentprocessing. An image reconstructor 34 receives sampled and digitizedx-ray data from DAS 32 and performs high-speed image reconstruction. Thereconstructed image is applied as an input to a computer 36 which storesthe image in a mass storage device 38.

[0030] Computer 36 also receives commands and scanning parameters froman operator via console 40 that has a keyboard. An associated cathoderay tube display 42 allows the operator to observe the reconstructedimage and other data from computer 36. The operator-supplied commandsand parameters are used by computer 36 to provide control signals andinformation to DAS 32, x-ray controller 28 and gantry motor controller30. In addition, computer 36 operates a table motor controller 44 whichcontrols a motorized table 46 to position patient 22 in gantry 12.Particularly, table 46 moves portions of patient 22 along a Z-axisthrough gantry opening 48.

[0031]FIG. 3 illustrates the x-ray tube 14 in greater detail. The X-raytube 14 includes an anode end 54, cathode end 56, and a center section58 positioned between anode end 54 and cathode end 56. The X-ray tube 14includes an X-ray tube insert 60 which is enclosed in a fluid-filledchamber 62 within a casing 64.

[0032] Electrical connections to x-ray tube insert 60 are providedthrough an anode receptacle 66 and a cathode receptacle 68. X-rays areemitted from x-ray tube 14 through a casing window 70 in casing 64 atone side of center section 58.

[0033] As shown in FIG. 4, the x-ray tube insert 60 includes a targetanode assembly 72 and a cathode assembly 74 disposed in a vacuum withina vacuum vessel 76. A stator 78 is positioned over vessel 76 adjacent toanode assembly 72. Upon the energization of the electrical circuitconnecting anode assembly 72 and cathode assembly 74, which produces apotential difference of, e.g., 60 kV to 140 kV, electrons are directedfrom cathode assembly 74 to anode assembly 72. The electrons striketarget anode assembly 72 and produce high frequency electromagneticwaves, or x-rays, and residual thermal energy. The x-rays are directedout through the casing window 70, which allows the x-rays to be directedtoward the object being imaged (e.g., the patient).

[0034]FIG. 5 illustrates a cross-sectional view of the anode assembly72. The anode assembly 72 includes a target 80, a bearing support 82, arear bearing assembly 84, and a front bearing assembly 85. The target 80is a metallic disk made of a refractory metal with graphite possiblybrazed to it. The target 80 provides a surface against which electronsfrom the cathode assembly 74 strike. In the exemplary embodiment, thetarget 80 rotates by the rotation of a bearing shaft 86. The rotation ofthe target 80 distributes the area on the target 80 which is bombardedby the electrons.

[0035] The bearing support 82 is a cylindrical tube which providessupport for the target anode assembly 72. The rear bearing assembly 84and the front bearing assembly 85 are located within bearing support 82.The target 80 is coupled to a bearing shaft 86 and rotates with thebearing shaft 86 about a tube axis of rotation 88. The target 80 and thebearing shaft 86 in combination form a rotatable assembly 90 that has acenter of gravity G which is located between (1) the target 80 and (2)the rear and front bearing assemblies 84 and 85. Thus, disposed alongthe tube axis of rotation 88 are, in order, the rear bearing assembly84, the front bearing assembly 85, the center of gravity G and thetarget 80.

[0036] During an imaging operation, the human patient 22 is receivedinside the gantry 12, and the x-ray tube 14 emits x-rays that passthrough the human patient 22 and that are received at the detector array18. This occurs as the gantry 12 rotates about the gantry axis ofrotation 24 and as the rotating assembly 90 rotates about the tube axisof rotation 88.

[0037] Specifically, and referring now also to FIGS. 6-8, as the gantry12 rotates about the gantry axis of rotation 24, the x-ray tube 14 alsorotates about the gantry axis of rotation 24 since the x-ray tube 14 ismounted to the gantry 12. As this occurs, a centrifugal force isdeveloped due to the rotation of the x-ray tube 14 about the gantry axisof rotation 24. The centrifugal force acts through the center of mass Gof the rotating assembly 90 to produce a first moment {right arrow over(M)}_(CF) that acts upon the x-ray tube 14.

[0038] Likewise, within the x-ray tube 14, the rotating assembly 90 alsorotates about the tube axis of rotation 88. Since the rotating assembly90 is part of the x-ray tube 14, the rotating assembly 90 simultaneouslyrotates about both the gantry axis of rotation 24 and the tube axis ofrotation 88. As shown in FIG. 7, the tube axis of rotation 88 isangularly displaced from the gantry axis of rotation 24 by a tilt angleθ. The rotating assembly 90 therefore precesses. During this precession,the tube axis of rotation 88 circumscribes an outer surface of a portionof a cone as the rotatable assembly 90 rotates about the gantry axis ofrotation 24.

[0039] The motion of the rotating assembly 90 is somewhat similar to themotion of a top spinning on a floor in that the top rapidly spins abouta first axis of rotation while simultaneously, but less rapidly,circumscribing a circle on the floor and thereby spinning about a secondaxis of rotation. A notable difference is that, in the case of a top,the precession is caused by gravity which produces a moment that actsupon the top. In the case of the x-ray tube 14, the precession is forcedby drive motors that drive rotation of the gantry 12 and the rotatingassembly 90. Therefore, whereas an input moment (caused by gravity)produces an output precession in the case of a top, an input precession(forced by drive motors) produces an output moment {right arrow over(M)}_(G) in the case of the rotating assembly 90. The output moment{right arrow over (M)}_(G) is a gyroscopic moment that acts upon thex-ray tube 14 and opposes the first moment {right arrow over (M)}_(CF).The output moment {right arrow over (M)}_(G) is produced by a pair offorces at the rear and front bearings 84 and 85 that are equal inmagnitude but opposite in direction. By suitably choosing a set ofoperating parameters, it is possible to make the net load on the rearand front bearings 84 and 85 be equal in magnitude. Assuming onecontinues to rotate the gantry at the same speed, it is thereforepossible to lower the load on the front bearing and hence to increasethe life of the bearing 85. This arrangement allows for greater controlof the relative loading of the rear bearing assembly 84 and the frontbearing assembly 85, which in turn allows bearing life to be increasedand/or higher speeds to be achieved.

[0040] Referring now to FIGS. 6-8, a mathematical description of theforces and moments developed, considering the gyroscopic effect, willnow be described. Of course, it should be understood that the followingmathematical description merely pertains to a preferred implementationof the invention, and other implementations are possible that would havea different mathematical description. In FIGS. 6-8, the rotatingassembly 90 is assumed to be rotating at uniform angular velocity andthe X-ray tube 14 rotates with the gantry 12 about the gantry axis 24.Additionally, in the mathematical description that follows, it isassumed that the gantry axis 24 may be tilted.

[0041] Table I below contains a description of the parameters shown inFIGS. 6-8. TABLE I X_(glob), Y_(glob), Z_(glob) Global axes with originO. Gantry 12 can tilt only about X_(glob). X_(gant), Y_(gant), Z_(gant)Gantry axes with origin O, such that, the gantry 12 rotates aboutZ_(gant) axis. X_(gant) is parallel to X_(glob). X′_(gant), Y′_(gant),Z′_(gant) Gantry axes with origin G. Z_(gant) and Z′_(gant) have samedirection. x_(an), y_(an), z_(an) Anode axes with origin G, such thatthe anode rotating assembly 90 rotates about z_(an) axis. G Center ofmass of the rotating assembly 90.

_(glob),

_(glob),

_(glob) Triad of unit vectors along X_(glob), Y_(glob), Z_(glob),respectively.

′_(gant),

′_(gant),

′_(gant) Triad of unit vectors along X′_(gant), Y′_(gant), Z′_(gant),respectively.

_(an),

_(an),

_(an) Triad of unit vectors along x_(an), y_(an), z_(an), respectively.A, B Locations at which the shaft 86 is supported by bearings 84 and 85,respectively. A_(x) Reaction perpendicular to the anode axis of rotation88 (z_(an)) and in the plane formed by the anode axis (z_(an)) ofrotation 88 and the gantry axis of rotation 24 (Z_(gant)), i.e.,reaction in the x_(an) − direction for bearing 84 at A. A_(y) Reactionperpendicular to the anode axis of rotation 88 and also perpendicular tothe plane formed by the anode axis of rotation (z_(an)) and the gantryaxis of rotation 24 (Z_(gant)), i.e., reaction in the y_(an) − directionfor bearing 84 at A. A_(z) Reaction along the anode axis of rotation 88,i.e., reaction in the z_(an) − direction for bearing 84 at A. B_(x)Reaction perpendicular to the anode axis of rotation 88 and in the planeformed by the axes of rotation 24 and 88 (z_(an) and Z_(gant)), i.e.,reaction in the x_(an) − direction for bearing 85 at B. B_(y) Reactionperpendicular to the anode axis of rotation 88 and also perpendicular tothe plane formed by the axes of rotation 24 and 88 (z_(an) andZ_(gant)), i.e., reaction in the y_(an) − direction for bearing 85 at B.B_(z) Reaction along the anode axis of rotation 88, i.e., reaction inthe z_(an) − direction for bearing 85 at B. I_(x) Mass Moment of inertiaof the rotating assembly 90 about x_(an) axis. I_(z) Mass Moment ofinertia of the rotating assembly 90 about z_(an) axis.

_(G) Resultant external force acting at point G of the rotating assembly90.

_(G) Angular momentum of the rotating assembly 90.

_(G) Moment vector about G.

_(G) is a gyroscopic moment.

_(CF) Moment vector about G.

_(CF) is produced by centrifugal force. a z_(an) co-ordinate of bearingat A with respect to local reference frame of anode. B z_(an)co-ordinate of bearing at B with respect to local reference frame ofanode. c z_(an) co-ordinate of focal spot with respect to localreference frame of anode. m Mass of the rotating assembly 90. gMagnitude of acceleration due to gravity. / Distance between bearings =a − b. r_(G) Distance of G from gantry Z_(gant) axis. α Gantry tiltangle, i.e., angle between gantry Z_(gant) axis and global Z_(glob)axis. θ Angle between the axes of rotation 24 and 88, i.e., gantryZ_(gant) axis and anode z_(an) axis. φ Angular position of tube on thegantry, i.e., angle between gantry X′_(gant) axis and global X_(glob)axis. _(ω1) Angular velocity of the gantry about Z_(gant) axis. _(ω2)Angular velocity of the anode about z_(an) axis.

[0042] It may be noted that parameters with a “

” sign represent vectors and same parameters represent magnitude if no “

” is included. Additionally, with respect to the distances a and b, ineach case, these distance are measured in a direction that is parallelto the axis of rotation of the anode 88 as shown in FIGS. 6-8. If thebearings 84 and 85 are to the left of the center of gravity G as shownin FIGS. 6-8, then the values of a and b are negative. Moreover, asindicated in Table 1, the parameter Z_(gant) refers to the gantry axisof rotation 24 and the parameter z_(an) refers to the anode axis ofrotation 88. In the description that follows, only the parameters z_(an)and Z_(gant) will be used to refer to the axes 24 and 88.

[0043] The gantry axis of rotation Z_(gant) and the anode axis ofrotation z_(an) are separated by an angle θ (the tilt angle) at anorigin ◯ which is the point of intersection. The gantry Y_(gant) andZ_(gant) axes lie in the Y_(glob) Z_(glob) plane and make an angle αwith Y_(glob) and Z_(gob) axes, respectively.

[0044] With reference to FIG. 6, the coordinate transformation principleyields the following equations: $\begin{matrix}{\begin{Bmatrix}X_{gant}^{\prime} \\Y_{gant}^{\prime} \\Z_{gant}^{\prime}\end{Bmatrix} = {\begin{bmatrix}{\cos \quad \theta} & {\cos \quad \frac{\pi}{2}} & {\cos \left( {\frac{\pi}{2} - \theta} \right)} \\{\cos \quad \frac{\pi}{2}} & {\cos \quad 0} & {\cos \quad \frac{\pi}{2}} \\{\cos \left( {\frac{\pi}{2} + \theta} \right)} & {\cos \quad \frac{\pi}{2}} & {\cos \quad \theta}\end{bmatrix}\begin{Bmatrix}x_{an} \\y_{an} \\z_{an}\end{Bmatrix}}} & \text{(1a)} \\{\begin{Bmatrix}X_{gant} \\Y_{gant} \\Z_{gant}\end{Bmatrix} = {\begin{bmatrix}{\cos \quad \varphi} & {\cos \quad \left( {\frac{\pi}{2} + \varphi} \right)} & {\cos \quad \frac{\pi}{2}} \\{\cos \quad \left( {\frac{\pi}{2} - \varphi} \right)} & {\cos \quad \varphi} & {\cos \quad \frac{\pi}{2}} \\{\cos \quad \frac{\pi}{2}} & {\cos \quad \frac{\pi}{2}} & {\cos \quad 0}\end{bmatrix}\begin{Bmatrix}X_{gant}^{\prime} \\Y_{gant}^{\prime} \\Z_{gant}^{\prime}\end{Bmatrix}}} & \text{(1b)} \\{\begin{Bmatrix}X_{glob} \\Y_{glob} \\Z_{glob}\end{Bmatrix} = {\begin{bmatrix}{\cos \quad 0} & {\cos \quad \frac{\pi}{2}} & {\cos \quad \frac{\pi}{2}} \\{\cos \quad \frac{\pi}{2}} & {\cos \quad \alpha} & {\cos \left( {\frac{\pi}{2} - \alpha} \right)} \\{\cos \quad \frac{\pi}{2}} & {\cos \left( {\frac{\pi}{2} + \alpha} \right)} & {\cos \quad \alpha}\end{bmatrix}\begin{Bmatrix}X_{gant} \\Y_{gant} \\Z_{gant}\end{Bmatrix}}} & \text{(1c)}\end{matrix}$

[0045] From the above equations, the relationship between anodecoordinates and gantry coordinates can be written as follows:$\begin{matrix}{\begin{Bmatrix}X_{gant}^{\prime} \\Y_{gant}^{\prime} \\Z_{gant}^{\prime}\end{Bmatrix} = {\begin{bmatrix}{\cos \quad \theta} & 0 & {\sin \quad \theta} \\0 & 1 & 0 \\{{- \sin}\quad \theta} & 0 & {\cos \quad \theta}\end{bmatrix}\begin{Bmatrix}x_{an} \\y_{an} \\z_{an}\end{Bmatrix}}} & (2)\end{matrix}$

[0046] The same relationship applies to the corresponding triad of unitvectors as expressed below: $\begin{matrix}{\begin{Bmatrix}{\overset{\rightarrow}{i}}_{gant}^{\prime} \\{\overset{\rightarrow}{j}}_{gant}^{\prime} \\{\overset{\rightarrow}{k}}_{gant}^{\prime}\end{Bmatrix} = {\begin{bmatrix}{\cos \quad \theta} & 0 & {\sin \quad \theta} \\0 & 1 & 0 \\{{- \sin}\quad \theta} & 0 & {\cos \quad \theta}\end{bmatrix}\begin{Bmatrix}{\overset{\rightarrow}{i}}_{an} \\{\overset{\rightarrow}{j}}_{an} \\{\overset{\rightarrow}{k}}_{an}\end{Bmatrix}}} & (3)\end{matrix}$

[0047] Equation (3) can be rewritten as follows:

{right arrow over (i)}′ _(gant)=(cos θ){right arrow over (i)} _(an)+(sinθ){right arrow over (k)} _(an) {right arrow over (j)}′ _(gant) ={rightarrow over (j)} _(an) {right arrow over (k)}′ _(gant)=(−sin θ){rightarrow over (i)} _(an)+(cos θ){right arrow over (k)} _(an)  (4)

[0048] Also, the relationship between global coordinates and the anodecoordinates can be deduced by matrix multiplication as follows:$\begin{matrix}{\begin{Bmatrix}x_{glob} \\y_{glob} \\z_{glob}\end{Bmatrix}{\quad{\begin{bmatrix}{\cos \quad {\varphi cos}\quad \theta} & {{- \sin}\quad \varphi} & {\cos \quad \varphi \quad \sin \quad \theta} \\{{\sin \quad {\varphi cos}\quad {\theta cos}\quad \alpha} - {\sin \quad {\alpha sin}\quad \theta}} & {\cos \quad \alpha \quad \cos \quad \varphi} & {{\sin \quad {\varphi sin}\quad {\theta cos\alpha}} + {\sin \quad {\alpha cos}\quad \theta}} \\{{{- \sin}\quad \varphi \quad \cos \quad \theta \quad \sin \quad \alpha} - {\cos \quad {\alpha sin}\quad \theta}} & {{- \sin}\quad \alpha \quad \cos \quad \varphi} & {{{- \sin}\quad \varphi \quad \sin \quad \theta \quad \sin \quad \alpha} + {\cos \quad \alpha \quad \cos \quad \theta}}\end{bmatrix}\begin{Bmatrix}x_{an} \\y_{an} \\z_{an}\end{Bmatrix}}}} & (5)\end{matrix}$

[0049] The same relationship applies to the corresponding triad of unitvectors as expressed below: $\begin{matrix}{\begin{Bmatrix}{\overset{\rightarrow}{i}}_{glob}^{\prime} \\{\overset{\rightarrow}{j}}_{glob}^{\prime} \\{\overset{\rightarrow}{k}}_{glob}^{\prime}\end{Bmatrix}{\quad{\quad{\begin{bmatrix}{\cos \quad {\varphi cos}\quad \theta} & {{- \sin}\quad \varphi} & {\cos \quad \varphi \quad \sin \quad \theta} \\{{\sin \quad {\varphi cos}\quad {\theta cos}\quad \alpha} - {\sin \quad {\alpha sin}\quad \theta}} & {\cos \quad \alpha \quad \cos \quad \varphi} & {{\sin \quad {\varphi sin}\quad {\theta cos\alpha}} + {\sin \quad {\alpha cos}\quad \theta}} \\{{{- \sin}\quad \varphi \quad \cos \quad \theta \quad \sin \quad \alpha} - {\cos \quad {\alpha sin}\quad \theta}} & {{- \sin}\quad \alpha \quad \cos \quad \varphi} & {{{- \sin}\quad \varphi \quad \sin \quad \theta \quad \sin \quad \alpha} + {\cos \quad \alpha \quad \cos \quad \theta}}\end{bmatrix}\begin{Bmatrix}{\overset{\rightarrow}{i}}_{an} \\{\overset{\rightarrow}{j}}_{an} \\{\overset{\rightarrow}{k}}_{an}\end{Bmatrix}}}}} & (6)\end{matrix}$

[0050] Equation (6) can be rewritten as follows: $\begin{matrix}\begin{matrix}{{\overset{\rightarrow}{i}}_{glob} = \quad {{\left( {\cos \quad \varphi \quad \cos \quad \theta} \right){\overset{\rightarrow}{i}}_{an}} + {\left( {{- \sin}\quad \varphi} \right){\overset{\rightarrow}{j}}_{an}} + {\left( {\cos \quad \varphi \quad \sin \quad \theta} \right){\overset{\rightarrow}{k}}_{an}}}} \\{{\overset{\rightarrow}{j}}_{glob} = \quad {{\left( {{\sin \quad \varphi \quad \cos \quad \theta \quad \cos \quad \alpha} - {\sin \quad \alpha \quad \sin \quad \theta}} \right){\overset{\rightarrow}{i}}_{an}} + {\left( {\cos \quad \alpha \quad \cos \quad \varphi} \right){\overset{\rightarrow}{j}}_{an}} +}} \\{\quad {\left( {{\sin \quad \varphi \quad \sin \quad \theta \quad \cos \quad \alpha} + {\sin \quad \alpha \quad \cos \quad \theta}} \right){\overset{\rightarrow}{k}}_{an}}} \\{{\overset{\rightarrow}{k}}_{glob} = \quad {{\left( {{{- \sin}\quad \varphi \quad \cos \quad \theta \quad \sin \quad \alpha} - {\cos \quad \alpha \quad \sin \quad \theta}} \right){\overset{\rightarrow}{i}}_{an}} + {\left( {{- \sin}\quad \alpha \quad \cos \quad \varphi} \right){\overset{\rightarrow}{j}}_{an}} +}} \\{\quad {\left( {{{- \sin}\quad \varphi \quad \sin \quad \theta \quad \sin \quad \alpha} + {\cos \quad \alpha \quad \cos \quad \theta}} \right){\overset{\rightarrow}{k}}_{an}}}\end{matrix} & (7)\end{matrix}$

[0051] With reference to FIG. 7, the gantry angular velocity {rightarrow over (ω)}₁ can be written as follows:

{right arrow over (ω)}₁=(−ω₁ sin θ){right arrow over (i)} _(an)+(ω₁ cosθ){right arrow over (k)} _(an)  (8)

[0052] The resultant anode angular velocity {right arrow over (ω)} maythen be written as follows:

{right arrow over (ω)}={right arrow over (ω)}₁+{right arrow over(ω)}₂=(−ω₁ sin θ){right arrow over (i)} _(an)+(ω₁ cos θ){right arrowover (k)} _(an)+ω₂ {right arrow over (k)} _(an)=(−ω₁ sin θ){right arrowover (i)} _(an)+(ω₁ cos θ+ω₂){right arrow over (k)} _(an)  (9)

[0053] Hence, the anode angular momentum {right arrow over (H)}_(G) canbe written as follows:

{right arrow over (H)} _(G) =I _(x)(−ω₁ sin θ){right arrow over (i)}_(an) +I _(z)(ω₁ cos θ+ω₂){right arrow over (k)} _(an)  (10)

[0054] Notably, the angular momentum {right arrow over (H)}_(G) isconstant (both in magnitude and direction). The resultant gyroscopicmoment {right arrow over (M)}_(G) on the rotating assembly 90 about itscenter of mass G can be written as follows: $\begin{matrix}{{\overset{\rightarrow}{M}}_{G} = {{\frac{}{t}\left( {\overset{\rightarrow}{H}}_{G} \right)} + {{\overset{\rightarrow}{\omega}}_{1}X\quad {\overset{\rightarrow}{H}}_{G}}}} & (11)\end{matrix}$

[0055] Therefore, substituting Eqs. (8) and (10) into Eq. (11) yieldsthe following equation: $\begin{matrix}\begin{matrix}{{\overset{\rightarrow}{M}}_{G} = \quad {0 + {{\left( {\omega_{1}\sin \quad \theta} \right)\left\lbrack {{I_{z}\left( {{\omega_{1}\cos \quad \theta} + \omega_{2}} \right)} - {I_{X}\left( {\omega_{1}\cos \quad \theta} \right)}} \right\rbrack}{\overset{\rightarrow}{j}}_{an}}}} \\{= \quad {{\left( {\omega_{1}\sin \quad \theta} \right)\left\lbrack {{I_{z}\left( {{\omega_{1}\cos \quad \theta} + \omega_{2}} \right)} - {I_{X}\left( {\omega_{1}\cos \quad \theta} \right)}} \right\rbrack}{\overset{\rightarrow}{j}}_{an}}}\end{matrix} & (12)\end{matrix}$

[0056] From Eq. (12), it is seen that when the tilt angle θ is equal tozero (θ=0), no gyroscopic moment is produced, that is, {right arrow over(M)}_(G)=O. When the tilt angle θ is equal to π/2(θ=π/2), then thegyroscopic moment is non-zero (specifically, {right arrow over(M)}_(G)=I_(z)ω₁ω₂{right arrow over (j)}_(an)).

[0057] If the anode is considered to be at an arbitrary position on thegantry (see FIG. 8), then the external force {right arrow over (F)}_(G)acting at the center of mass G of the rotating assembly 90 can bewritten as follows:

{right arrow over (F)} _(G)=mr_(Gω1) ² {right arrow over (i)}′_(gant)−mg {right arrow over (j)} _(glob)  (13)

[0058] Combining Eqs. (4), (7) and (13) yields the following equations:$\begin{matrix}{{\overset{\rightarrow}{F}}_{G} = {{{mr}_{G}{\omega_{1}^{2}\left\lbrack {{\left( {\cos \quad \theta} \right){\overset{\rightarrow}{i}}_{an}} + {\left( {\sin \quad \theta} \right){\overset{\rightarrow}{k}}_{an}}} \right\rbrack}} - {{mg}\left\lbrack {{\left( {{\sin \quad {\varphi cos}\quad \theta \quad \cos \quad \alpha} - {\sin \quad \alpha \quad \sin \quad \theta}} \right){\overset{\rightarrow}{i}}_{an}} + {\left( {\cos \quad \alpha \quad \cos \quad \varphi} \right){\overset{\rightarrow}{j}}_{an}} + {\left( {{\sin \quad \varphi \quad \sin \quad \theta \quad \cos \quad \alpha} + {\sin \quad \alpha \quad \cos \quad \theta}} \right){\overset{\rightarrow}{k}}_{an}}} \right\rbrack}}} & (14) \\{{\overset{\rightarrow}{F}}_{G} = {{\left\lbrack {{{mr}_{G}\omega_{1}^{2}\cos \quad \theta} - {{mg}\left( {{\sin \quad \varphi \quad \cos \quad \theta \quad \cos \quad \alpha} - {\sin \quad \alpha \quad \sin \quad \theta}} \right)}} \right\rbrack {\overset{\rightarrow}{i}}_{an}} - {{{mg}\left( {\cos \quad \alpha \quad \cos \quad \varphi} \right)}{\overset{\rightarrow}{j}}_{an}} + {\quad{\left\lbrack {{{mr}_{G}\omega_{1}^{2}\quad \sin \quad \theta} - {{mg}\left( {{\sin \quad \varphi \quad \sin \quad \theta \quad \cos \quad \alpha} + {\sin \quad \alpha \quad \cos \quad \theta}} \right)}} \right\rbrack {\overset{\rightarrow}{k}}_{an}}}}} & (15)\end{matrix}$

[0059] With regard to Eqs. (14) and (15), the following cases are ofparticular interest. First, when the angle φ (i.e., angle between gantryaxis X′_(gant) and global axis X_(glob)) is equal to π/2 (z_(an) axisupwards with respect to Z_(gant) axis in the vertical plane) then theexternal force {right arrow over (F)}_(G) acting at the center of mass Gof the rotating assembly 90 can be written as follows:

{right arrow over (F)} _(G)=[mr_(G)ω₁ ² cos θ−mg cos(α+θ)]{right arrowover (i)} _(an)+[mr_(G)ω₁ ² sin θ−mg sin(α+θ)]{right arrow over (k)}_(an)

[0060] Second, when the angle φ is equal to −π/2 (z_(an) axis downwardswith respect to Z_(gant) axis in the vertical plane) then the externalforce {right arrow over (F)}_(G) acting at the center of mass G of therotating assembly 90 can be written as follows:

{right arrow over (F)} _(G)=[mr_(G)ω₁ ² cos θ+mg cos(θ−α)]{right arrowover (i)} _(an)+[mr_(G)ω₁ ² sin θ+mg sin(θ−α)]{right arrow over (k)}_(an)

[0061] Assuming {right arrow over (A)} and {right arrow over (B)} aredefined as the reaction forces at the bearings located at A and B,respectively, and the sum of all the forces must be zero, then thefollowing equation must be true:

{right arrow over (A)}+{right arrow over (B)}+{right arrow over (F)}_(G) =O  (16)

[0062] Substituting for {right arrow over (F)}_(G) from Eq. (15) yieldsthe following equations:

A _(x) +B _(x)+[mr_(G)ω₁ ² cos θ−mg(sin φ cos θ cos α−sin α sinθ)]=O  (17a)

A _(y) +B _(y)−mg (cos α cos φ)=0  (17b)

A _(z) +B _(z)+[mr_(G)ω₁ ² sin θ−mg(sin φ sin θ cos α+sin α cosθ)]=O  (17c)

[0063] Computing moments about the center of gravity G yields thefollowing equation:

(a{right arrow over (k)} _(an) X{right arrow over (A)})+(b{right arrowover (k)} _(an) X{right arrow over (B)})+{right arrow over (M)} _(G)=O  (18)

[0064] Substituting for {right arrow over (M)}_(G) from Eq. (12) yieldsthe following equations:

aA _(x) +bB _(x)+(ω₁ sin θ)[I _(z)(ω₁ cos θ+ω₂)−I _(x)(ω₁ cosθ)]=O  (19a)

aA _(y) +bB _(y) =O  (19b)

[0065] Solving for A_(x) and B_(x) simultaneously from Eqs. (17a) and(19a) yields the following equations: $\begin{matrix}\begin{matrix}{A_{x} = \quad \frac{- {\left( {\omega_{1}\quad \sin \quad \theta} \right)\left\lbrack {{I_{z}\left( {{\omega_{1}\cos \quad \theta} + \omega_{2}} \right)} - {I_{x}\omega_{1}\cos \quad \theta}} \right\rbrack}}{\left( {a - b} \right)}} \\{\quad \frac{+ {{mb}\left\lbrack \left. {{r_{G}\omega_{1}^{2}\cos \quad \theta} - {g\left( {{\sin \quad \varphi \quad \cos \quad {\theta cos}\quad \alpha} - {\sin \quad \alpha \quad \sin \quad \theta}} \right.}} \right\rbrack \right.}}{\left( {a - b} \right)}}\end{matrix} & \text{(20a)} \\\begin{matrix}{B_{x} = \quad \frac{\left( {\omega_{1}\sin \quad \theta} \right)\left\lbrack {{I_{z}\left( {{\omega_{1}\cos \quad \theta} + \omega_{2}} \right)} - {I_{x}\omega_{1}\cos \quad \theta}} \right\rbrack}{\left( {a - b} \right)}} \\{\quad \frac{- {{ma}\left\lbrack {{r_{G}\omega_{1}^{2}\quad \cos \quad \theta} - {g\left( {{\sin \quad \varphi \quad \cos \quad {\theta cos}\quad \alpha} - {\sin \quad \alpha \quad \sin \quad \theta}} \right)}} \right\rbrack}}{\left( {a - b} \right)}}\end{matrix} & \text{(20b)}\end{matrix}$

[0066] Solving for A_(y) and B_(y) simultaneously from Eqs. (17b) and(19b) yields the following equations: $\begin{matrix}{A_{y} = \frac{{- {mbg}}\quad \cos \quad \alpha \quad \cos \quad \varphi}{\left( {a - b} \right)}} & \text{(21a)} \\{B_{y} = \frac{{mag}\quad \cos \quad \alpha \quad \cos \quad \varphi}{\left( {a - b} \right)}} & \text{(21b)}\end{matrix}$

[0067] It may be noted that there is only one equation (Eq. 17c) andthere are two variables (A_(z) and B_(z)). For purposes of consideringthe axial forces applied to the bearings, the following considerationsmay be kept in mind. First, the worst case is when A_(z)=O or B_(z)=O,that is, when all the axial force is applied to one bearing. Second, ifone bearing is a deep groove ball bearing and the other bearing is anangular contact bearing, then all the axial force will be borne byangular contact bearing only. Third, for the purpose of assembly, ifthere is a stepped shaft, as illustrated in FIGS. 9A-9B, a small amountof axial “play” should be maintained to allow rotation (otherwise theassembly may become jammed). In this case, the axial force is applied toonly one bearing.

[0068] In view of the above, one of the two following sets of conditionswill be true:

A _(z)=−mr_(G)ω₁ ² sin θ+mg(sin φ sin θ cos α+sin α cos θ)  (22a)

B _(z)=0  (22b)

[0069] or

A _(z)=0  (23a)

B _(z)=−mr_(G)ω₁ ² sin θ+mg(sin φ sin θ cos α+sin α cos θ)  (23b)

[0070] For the ongoing analysis, consider Eqs. (23a)-(23b) will beconsidered.

[0071] To examine geometrical constraints, assume that r_(P1) is theradius of the point of incidence with respect to the gantry Z_(gant)axis, r_(P2) is the point of incidence with respect to the anode z_(an)axis, and c is the distance of the center of the extreme anode surfacefrom the center of mass of the anode. It may then be noted that thepoint of incidence lies on the plane formed by gantry Z_(gant) axis andanode z_(an) axis. Thus, for the purpose of analysis, this plane may beconsidered as shown in FIG. 10. From FIG. 10,

r _(G) +c sin θ=r _(P1) +r _(P2) cos θ  (24)

[0072] Hence,

r _(G) =r _(P1) +r _(P2) cos θ−c sin θ  (25)

[0073] Referring again to Eqs. (20a)-(20b) and (21a)-(21b), it may benoted that the effects of gravity are relatively minor as compared tothe effects of the moments M_(G) and M_(CF), especially at higherspeeds. If the effects of gravity are ignored in Eqs. (20a)-(20b) and(21a)-(21b), then the force in the y-direction is equal to zero (Eqs.(21a)-(21b)) and Eqs. (20a)-(20b) may be simplified as follows:$\begin{matrix}{A_{x} = \frac{{- {\left( {\omega_{1}\sin \quad \theta} \right)\left\lbrack {{I_{z}\left( {\omega_{2} + {\omega_{1}\quad \cos \quad \theta}} \right)} - {I_{x}\omega_{1}\quad \cos \quad \theta}} \right\rbrack}} + {{mb}\left\lbrack {r_{G}\omega_{1}^{2}\cos \quad \theta} \right\rbrack}}{\left( {a - b} \right)}} & \text{(26a)} \\{B_{x} = \frac{{\left( {\omega_{1}\sin \quad \theta} \right)\left\lbrack {{I_{z}\left( {\omega_{2} + {\omega_{1}\cos \quad \theta}} \right)} - {I_{x}\omega_{1}\cos \quad \theta}} \right\rbrack} + {{ma}\left\lbrack {r_{G}\omega_{1}^{2}\cos \quad \theta} \right\rbrack}}{\left( {a - b} \right)}} & \text{(26b)}\end{matrix}$

[0074] With respect to the force A_(X) applied to the rear bearingassembly 84, this force can be broken down into two components asfollows: $\begin{matrix}{A_{X1} = \frac{{mb}\left\lbrack {r_{G}\omega_{1}^{2}\cos \quad \theta} \right\rbrack}{\left( {a - b} \right)}} & \text{(27a)} \\{A_{X2} = \frac{- {\left( {\omega_{1}\sin \quad \theta} \right)\left\lbrack {{I_{z}\left( {\omega_{2} + {\omega_{1}\cos \quad \theta}} \right)} - {I_{x}\omega_{1}\cos \quad \theta}} \right\rbrack}}{\left( {a - b} \right)}} & \text{(27b)}\end{matrix}$

[0075] where A_(X1) is the load applied to the rear bearing assembly 84due to the centrifugal force in reaction to centripetal acceleration andA_(X2) is the load applied to the rear bearing assembly 84 due to thegyroscopic moment M_(G).

[0076] Likewise, with respect to the force F_(B) applied to the frontbearing assembly 85, this force can be broken down into two componentsas follows: $\begin{matrix}{B_{X1} = \frac{- {{ma}\left\lbrack {r_{G}\omega_{1}^{2}\cos \quad \theta} \right\rbrack}}{\left( {a - b} \right)}} & \text{(28a)} \\{B_{X2} = \frac{\left( {\omega_{1}\sin \quad \theta} \right)\left\lbrack {{I_{z}\left( {\omega_{2} + {\omega_{1}\cos \quad \theta}} \right)} - {I_{x}\omega_{1}\cos \quad \theta}} \right\rbrack}{\left( {a - b} \right)}} & \text{(28b)}\end{matrix}$

[0077] where B_(X1) is the load applied to the front bearing assembly 85due to the centrifugal force and B_(X2) is the load applied to the frontbearing assembly 85 due to the gyroscopic moment M_(G).

[0078] Based on how the x-ray tube 14 is mounted to the gantry (that is,depending on the tilt angle), it is possible to adjust the relativeloading of the rear and front bearing assemblies 84 and 85. Theparameters of Eqs. (26a)-(26b) can be optimized based on the applicationto achieve a particular gantry speed or to achieve a particular relativeloading between the rear and front bearings 84 and 85. Once theremaining parameters of Eqs. (26a)-(26b) are decided upon, Eqs.(26a)-(26b) can be solved to derive the correct tilt angle. If desired,Eqs. (20a)-(20b) and (21a)-(21b) may be used instead, although theeffects of gravity are relatively minor as compared to the effects ofthe centrifugal force and gyroscopic moment (as previously noted). Eqs.(22a)-(22b), (23a)-(23b), (24) and (25) may be taken into account inconnection with axial loading when constructing the bearing assemblies84 and 85. In this regard, it may be noted that the bearing assemblies84 and 85 may need to be constructed to handle additional load in theaxial direction due to the tilting of the anode axis relative to thegantry axis.

[0079] Referring now to FIG. 11, FIG. 11 is a graph of the anode tiltangle θ required to maintain constant front bearing load as a functionof gantry rotation time for an exemplary anode construction. Curve 100is the anode tilt angle θ (in degrees, left axis), curve 102 is theradial load (in Newtons, right axis) applied to the front bearing 85,curve 104 is the radial load (in Newtons, right axis) applied to thefront bearing 84, and curve 106 is the axial load (in Newtons, rightaxis) applied to the front bearing 85. As shown in FIG. 11, as gantryrotation time decreases (or gantry speed increases), the tilt angle θcan be increased to increase the magnitude of the loading experienced bythe rear bearing assembly 84. This allows the total loading experiencedby the bearings 84 and 85 to increase without exceeding the design limitof bearing 85.

[0080] The tilt angle preferably has a magnitude which is greater than2° and less than 70°. For example, the tilt may have a magnitude whichis greater than 5° and less than 50°, or more preferably less than 20°.According to this arrangement, it is possible to achieve a more balancedloading between the rear bearing assembly 84 and the front bearingassembly 85, rather than having the front bearing assembly bear most ofthe load. For example, the loading that is experienced by the rearbearing assembly 84 may be one tenth (i.e., an order of magnitude lessthan) that at the front bearing assembly 85. Preferably, the loading isexperienced by the rear bearing assembly 84 is at least half orthree-quarters as large as loading experienced by the front bearingassembly 85. Most preferably, the rear bearing 84 and the front bearing85 are approximately equally loaded. In FIG. 11, equal loading occurs ata gantry rotation time of about 0.295 sec (or rotation speed of about3.4 Hz) with a tilt angle of about 14°.

[0081] Referring now to FIGS. 12A-12C, FIGS. 12A-12C pictoriallydescribe how the balanced loading is achieved. Initially, it may benoted that the vectors shown in FIGS. 12A-12C are not shown in thepositive direction but in the actual direction based on the geometryshown. FIG. 12A shows the forces A_(X1) and B_(X1) applied to thebearing shaft in the location of bearings 84 and 85 as a result of thecentrifugal force. As shown, the force B_(X1) is much larger than theforce A_(X1), which is also in the opposite direction. FIG. 12B showsthe forces A_(X2) and B_(X2) applied to the bearing shaft at bearings 84and 85, respectively, as a result of the gyroscopic moment M_(G). Asshown in FIG. 12B, the force B_(X2) opposes the force B_(X1), and thereduction in force applied to the bearing 85 is compensated by anincrease in the force A_(X2) applied at the bearing 84. As a result, asshown in FIG. 12C, the net force A_(X) applied to the bearing 84 isapproximately equal to the net force B_(X) applied to the bearing 85.

[0082] Referring now to FIGS. 13A-13C, operation of the above-describedto improve imaging is shown. FIG. 13A shows deflection of the target 80due to centrifugal force. During scanning, the centrifugal force on thetarget 80 causes the target 80 to deflect outward away from the gantryrotation axis a distance of Z₁. This causes the focal spot 110 of thex-ray beam that is reflected by the target 80 to move in the z-directionto a position 110′. As shown in FIG. 13B, the gyroscopic moment M_(G)applies an opposing force which causes the target 80 to deflect in theopposite direction a distance of Z₂. Therefore, as shown in FIG. 13C,the net deflection is greatly reduced and approaches zero. Because thenet deflection is greatly reduced by the production of the gyroscopicmoment M_(G), movement of the focal spot 110 is greatly reduced. Thetilted rotating assembly 90 therefore serves not just to emit thex-rays, but also to gyroscopically stabilize the focal spot 110 of thex-ray beam. The benefit of the two counter-balancing forces is that thefocal spot 110 moves much less in the z-direction and hence under allscanning procedures, the focal spot 110 remains much more fixed withrespect to the detector. This stability in the focal spot position leadsto better image quality.

[0083] While the embodiments illustrated in the Figures and describedabove are presently preferred, it should be understood that theseembodiments are offered by way of example only. The invention is notlimited to a particular embodiment, but extends to variousmodifications, combinations, and permutations that nevertheless fallwithin the scope and spirit of the appended claims.

What is claimed is:
 1. A computed tomography system comprising: (A) agantry, said gantry rotating about a gantry axis of rotation; (B) anx-ray tube, said x-ray tube being mounted to said gantry, said x-raytube comprising a rotatable assembly having a tube axis of rotation,said tube axis of rotation being angularly displaced from said gantryaxis of rotation by a tilt angle; wherein rotation of said x-ray tubeabout said gantry axis of rotation causes a centrifugal force to beapplied to said rotatable assembly, said centrifugal force producing afirst moment; and wherein rotation of said rotatable assembly about saidtube axis of rotation produces a second moment that opposes said firstmoment.
 2. A computed tomography system according to claim 1, whereinsaid x-ray tube further comprises a first bearing assembly and a secondbearing assembly; wherein said second bearing assembly is located alongsaid tube axis of rotation between said first bearing assembly and acenter of gravity of said rotatable assembly; and wherein, duringrotation of said x-ray tube about said gantry axis of rotation andduring said rotation of said rotatable assembly about said tube axis ofrotation, said first and second bearing assemblies experienceapproximately equal loading.
 3. A computed tomography system accordingto claim 1, wherein said x-ray tube further comprises a first bearingassembly and a second bearing assembly; wherein said second bearingassembly is located along said tube axis of rotation between said firstbearing assembly and a center of gravity of said rotatable assembly; andwherein, during rotation of said x-ray tube about said gantry axis ofrotation and during said rotation of said rotatable assembly about saidtube axis of rotation, said first bearing assembly experiences loadingthat is at least one tenth as large as loading experienced by saidsecond bearing assembly.
 4. A computed tomography system according toclaim 3 wherein, during rotation of said x-ray tube about said gantryaxis of rotation and during said rotation of said rotatable assemblyabout said tube axis of rotation, said first bearing assemblyexperiences loading that is at least three-quarters as large as loadingexperienced by said second bearing assembly.
 5. A computed tomographysystem according to claim 4, further comprising an x-ray detector, saiddetector being mounted to said gantry, and wherein said x-ray tube emitsx-rays that are detected by said x-ray detector while said rotatableassembly rotates about said tube axis of rotation to produce said secondmoment that opposes said first moment.
 6. A computed tomography systemaccording to claim 1, wherein said tilt angle has a magnitude which isgreater than 2°.
 7. A computed tomography system according to claim 1,wherein said tilt angle has a magnitude which is greater than 5°.
 8. Acomputed tomography system according to claim 1, wherein said tilt anglehas a magnitude which is greater than 5° and less than 20°.
 9. Acomputed tomography system according to claim 1, wherein said gantryrotates at a gantry rotational speed; and wherein said second moment isa gyroscopic moment that is produced by precession of said rotatableassembly, said precession occurring by way of said rotation of saidx-ray tube about said gantry axis of rotation and said rotation of saidrotatable assembly about said tube axis of rotation, said tube axis ofrotation of said rotatable assembly circumscribing an outer surface of aportion of a cone as said rotatable assembly rotates about said gantryaxis of rotation.
 10. A method of operating a computed tomography systemcomprising: producing a first moment that acts upon an x-ray tube, saidfirst moment being produced by rotation of a gantry about a gantry axisof rotation at a gantry rotational speed, said x-ray tube being mountedto said gantry; producing a second moment that acts upon said x-ray tubewhile said first moment is being produced, said second moment beingproduced by rotation of a rotating assembly of said x-ray tube about atube axis of rotation, said tube axis of rotation being angularlydisplaced from said gantry axis of rotation by a tilt angle; whereinsaid second moment is a gyroscopic moment that is produced by precessionof said rotatable assembly, said precession occurring by way of saidrotation of said x-ray tube about said gantry axis of rotation and saidrotation of said rotatable assembly about said tube axis of rotation,and said tube axis of rotation of said rotatable assembly circumscribingan outer surface of a portion of a cone as said rotatable assemblyrotates about said gantry axis of rotation.
 11. A method according toclaim 10, wherein said tilt angle has a magnitude which is greater than2° and less than 70°.
 12. A method according to claim 10, wherein saidtilt angle has a magnitude which is greater than 5° and less than 20°.13. A method according to claim 10, wherein said tilt angle has amagnitude which is greater than 2°.
 14. A method according to claim 10,further comprising receiving a human patient inside said gantry, andwherein x-ray tube emits x-rays that pass through said human patient andare received at a detector during said producing steps.
 15. A methodaccording to claim 10, wherein said step of producing said second momentstabilizes the focal spot position of an x-ray beam of said x-ray tube.16. A method of operating a computed tomography system comprising:producing a first moment that acts upon an x-ray tube, said first momentbeing produced by rotation of a gantry about a gantry axis of rotation,said x-ray tube being mounted to said gantry; producing a second momentthat acts upon said x-ray tube while said first moment is beingproduced, said second moment being produced by rotation of a rotatingassembly of said x-ray tube about a tube axis of rotation, said tubeaxis of rotation being angularly displaced from said gantry axis ofrotation by a tilt angle; and wherein said tilt angle has a magnitudewhich is greater than 2°.
 17. A computed tomography system comprising:(A) a gantry, said gantry rotating about a gantry axis of rotation at agantry rotational speed; (B) an x-ray tube, said x-ray tube beingmounted to said gantry, said x-ray tube comprising (1) a vacuum vessel;(2) an anode assembly, said anode assembly being disposed in said vacuumvessel, said anode assembly including (a) a first bearing assembly; (b)a second bearing assembly; (c) a rotatable assembly including (i) arotatable shaft, said rotatable shaft being rotatably mounted withinsaid vacuum vessel by way of said first and second bearing assemblies,said rotatable shaft defining a tube axis of rotation, said tube axis ofrotation being angularly displaced from said gantry axis of rotation bya tilt angle; (ii) a target, said target being coupled to said shaft androtating with said shaft, said target and said first bearing assemblybeing disposed on opposite sides of said second bearing assembly alongsaid tube axis of rotation; and (3) a cathode assembly, said cathodeassembly being disposed in said vacuum vessel at a distance from theanode assembly, said cathode assembly being configured to emit electronsthat bombard said target to produce x-rays; wherein a center of gravityof said rotatable assembly is located between (a) said target and (b)said first and second bearing assemblies; wherein rotation of saidrotatable assembly about said gantry axis of rotation causes acentrifugal force to be applied to said rotatable assembly, saidcentrifugal force producing a first moment; and wherein rotation of saidrotatable assembly about said tube axis of rotation produces a secondmoment that opposes said first moment.
 18. A computed tomography systemaccording to claim 17, wherein said gantry rotates at a gantryrotational speed; and wherein said second moment is a gyroscopic momentthat is produced by precession of said rotatable assembly, saidprecession occurring by way of said rotation of said x-ray tube aboutsaid gantry axis of rotation and said rotation of said rotatableassembly about said tube axis of rotation, said tube axis of rotation ofsaid rotatable assembly circumscribing an outer surface of a portion ofa cone as said rotatable assembly rotates about said gantry axis ofrotation.
 19. A computed tomography system according to claim 17,wherein said tilt angle has a magnitude which is greater than 2° andless than 50°.
 20. A computed tomography system according to claim 17,wherein said tilt angle has a magnitude which is greater than 5° andless than 20°.
 21. A computed tomography system according to claim 17wherein, during rotation of said x-ray tube about said gantry axis ofrotation and during said rotation of said rotatable assembly about saidtube axis of rotation, said first bearing assembly experiences loadingthat is at least three-quarters as large as loading experienced by saidsecond bearing assembly.
 22. A computed tomography system according toclaim 17, further comprising an x-ray detector, said detector beingmounted to said gantry, and wherein said x-ray tube emits x-rays thatare detected by said x-ray detector while said rotatable assemblyrotates about said tube axis of rotation to produce said second momentthat opposes said first moment.
 23. A computed tomography systemcomprising: (A) means for generating x-rays, said x-rays being emittedfrom said means for generating in the form of an x-ray beam having afocal spot, and said means for generating including a means forgyroscopically stabilizing a position of said focal spot of said x-raybeam; and (B) means for detecting said x-rays generated by said meansfor generating.
 24. A computed tomography system comprising: (A) agantry, said gantry rotating about a gantry axis of rotation; (B) anx-ray tube, said x-ray tube being mounted to said gantry, said x-raytube comprising a rotatable assembly having a tube axis of rotation,said tube axis of rotation being angularly displaced from said gantryaxis of rotation by a tilt angle; wherein rotation of said x-ray tubeabout said gantry axis of rotation causes a centrifugal force to beapplied to said rotatable assembly; and wherein rotation of saidrotatable assembly about said tube axis of rotation produces agyroscopic moment that results in an additional force being applied tosaid rotatable assembly that opposes said centrifugal force.